Simultaneous Flows Through a Communication Network

This paper presents a generalization of the results of Elias, Feinstein, and Shannon, and Ford and Fulkerson on the maximum rate of information flow through a communciation network. The problem which is considered is the following: suppose a fixed rate of flow of information is being maintained between a pair of stations
A
and
B
of a communication network, then 1) what is the maximum rate of flow of information between another pair of stations
C
and
D
of the same communication network, and 2) how can one allocate, among the channels, the original load on the communciation network to obtain the maximal flow between stations
C
and
D
. It is shown that within certain determinable limits the sum of these two rates of flow remains a constant. A technique for attaining the maximal flow between stations
C
and
D
based upon the linear programming is described. A solution of the generalization of this problem to the case of
k
simultaneous flows is also presented.